Least Common Multiple (LCM) of 119 and 137
The least common multiple (LCM) of 119 and 137 is 16303.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 119 and 137?
First, calculate the GCD of 119 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 137 = 0 remainder 119 |
| 2 | 137 ÷ 119 = 1 remainder 18 |
| 3 | 119 ÷ 18 = 6 remainder 11 |
| 4 | 18 ÷ 11 = 1 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 48 | 1200 |
| 150 and 115 | 3450 |
| 69 and 178 | 12282 |
| 105 and 193 | 20265 |
| 170 and 142 | 12070 |